John Mothersole, council chief executive, said: “We can only fund 11 community libraries plus Central Library.

“We thought up to 14 could close, but that has been increased because we face deeper budget cuts than expected.”

“There are 27 organisations who have expressed an interest in running libraries – although we do not want to name them at this stage, because they would then come under a lot of pressure.

“We also know there are a lot of people and voluntary groups willing to run libraries and we have funding set aside to allow some of them to do so.

“The ideal scenario would be where we do not have to close any libraries at all.”

Under the plans, the city’s mobile library service will stop next year, while Tinsley Library will remain open until 2016 due to a lease agreement on the building.

Levels of deprivation, library use and distance from other facilities in each area were some of the criteria used by council bosses in drawing up the proposals.

The council said it is willing to allow community groups or other organisations to take over any of the 15 threatened sites and is inviting expressions of interest when public consultation begins next month.

Funding is being set aside to cover operating costs – excluding staff – at up to five sites for two years.

Libraries earmarked to be ‘community-run’ are Newfield Green, Burngreave, Park, Southey and Woodhouse, due to interest from community groups, although no decision has been made.

Coun Mazher Iqbal, cabinet member for communities, said: “These proposals are the fairest we can achieve for Sheffield right now.”

The council said those wishing to run libraries would have to allow freedom of access.